"Our case STRONGLY continues,we will keep up the good...fight,and I believe we will prevail!"he wrote.
"Nevertheless,in the best interest of our Country,I am recommending that Emily and her team do what needs to be done with regard to initial protocols,and have told my team to do the same."
In her letter to Biden,Murphy said she had not been pressured by anyone in the Trump administration to delay the transition process.
"Contrary to media reports and insinuations,my decision was not made out of fear or favouritism,"she wrote.
"I strongly believe that the statute requires the GSA Administrator ascertain,not impose,the apparent president-elect."
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She stressed that she was not empowered to officially determine the election winner,and that her role was limited to the question of making resources available during a transition.
Biden's top transition adviser Yohannes Abraham said:"Today’s decision is a needed step to begin tackling the challenges facing our nation,including getting the pandemic under control and our economy back on track.
"In the days ahead,transition officials will begin meeting with federal officials to discuss the pandemic response,have a full accounting of our national security interests,and gain complete understanding of the Trump administration’s efforts to hollow out government agencies."
Earlier in the day,Biden announcedhis nominees for several key cabinet positions including secretary-of-state,national security adviser and director of national intelligence.
Biden signalled that climate change would be a major focus for his administration by naming John Kerry,the former secretary-of-state and presidential nominee,as his special presidential envoy for climate.
Many of Biden's nominees served in senior roles in the Obama administration,a trend likely to continue with subsequent cabinet choices.The Wall Street Journal reported on Tuesday (AEDT) that Biden will choose Janet Yellen - whom Barack Obama appointed to lead the US Federal Reserve - to be his treasury secretary.
As expected,Biden chose Antony Blinken to be his secretary-of-state,a role equivalent to foreign affairs minister,and Jake Sullivan to be his national security adviser.
Other nominees include Alejandro Mayorkas,the first Latino and immigrant ever nominated to serve as secretary of homeland security.
Biden has chosen veteran diplomat Linda Thomas-Greenfield,who is black,to be his ambassador to the United Nations and Avril Haines to be his director of national intelligence. Haines would be the first woman to serve in this role.
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